# Group 82944.gr downloaded from the LMFDB on 20 October 2025. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation GPerm is permutation group 
#	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
# Many characteristics of the group are stored as booleans in a record: 
#	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 
# The character table is stored as a record chartbl_n_i where n is the order 
# of the group and i is which group of that order it is. The record is 
# converted to a character table using ConvertToLibraryCharacterTableNC 

 
# Constructions 
GPC := PcGroupCode(54700764691967235687223887227641479940660580184216201439864896604809508505083305936706187053148278505920863469222531013189667712578834279567529077481289202520615059156356714427817073747347011873026872244165537575843021753206860728819589964638571912645446998579105786705321329996138116054322788617324689,82944); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.8; f := GPC.9; g := GPC.11; h := GPC.12;
GPerm := Group( (10,11)(12,15)(13,17)(14,16), (13,17)(14,16), (1,2,4)(3,6,8)(5,7,9), (2,4)(5,9)(6,8)(10,12)(11,15)(13,14)(16,17), (2,5,3)(4,6,7), (10,13)(11,16)(12,14)(15,17), (10,14)(11,16)(12,13)(15,17), (10,12)(11,15)(13,14)(16,17), (10,13)(12,14), (1,3,7)(2,6,9)(4,8,5) );

 
# Booleans 
booleans_82944_gr := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_82944_gr:=rec(); 
chartbl_82944_gr.IsFinite:= true; 
chartbl_82944_gr.UnderlyingCharacteristic:= 0; 
chartbl_82944_gr.UnderlyingGroup:= GPerm;
chartbl_82944_gr.Size:= 82944;
chartbl_82944_gr.InfoText:= "Character table for group 82944.gr downloaded from the LMFDB."; 
chartbl_82944_gr.Identifier:= " C6^2:C2^2.S4^2 "; 
chartbl_82944_gr.NrConjugacyClasses:= 143; 
chartbl_82944_gr.ConjugacyClasses:= [(), (10,12)(11,15)(13,14)(16,17), (11,15)(13,14), (10,13)(11,16)(12,14)(15,17), (10,13)(11,17)(12,14)(15,16), (2,4)(3,7)(5,6)(8,9), (2,4)(3,7)(5,6)(8,9)(10,12)(11,15)(13,14)(16,17), (13,16)(14,17), (10,11)(12,15)(13,14)(16,17), (1,6)(2,7)(3,9), (1,6)(2,7)(3,9)(10,12)(11,15)(13,14)(16,17), (1,9)(2,7)(3,6)(4,5)(10,17)(11,14)(12,16)(13,15), (1,8)(2,6)(3,4)(5,7)(10,12)(16,17), (1,6)(2,3)(4,8)(7,9)(10,13)(11,17)(12,14)(15,16), (2,4)(3,7)(5,6)(8,9)(10,12)(11,13)(14,15)(16,17), (1,7)(2,5)(4,9)(6,8)(13,17)(14,16), (2,4)(5,9)(6,8)(11,15)(16,17), (2,4)(5,9)(6,8)(10,17)(11,14)(12,16)(13,15), (1,9)(3,5)(4,6)(10,17)(11,13)(12,16)(14,15), (2,4)(5,9)(6,8)(10,17)(11,15)(12,16)(13,14), (1,9)(2,5)(4,7)(10,15)(11,12), (1,3,7)(2,6,9)(4,8,5), (2,8,7)(3,4,9), (10,13,15)(11,12,14), (1,3,6)(2,4,9)(5,7,8), (1,4,2)(3,8,6)(5,9,7)(10,13,15)(11,12,14), (2,3,5)(4,7,6)(11,13,16)(14,17,15), (1,7,2)(3,8,4)(5,9,6)(10,13,11)(12,14,15), (10,15,12,11)(13,17,14,16), (11,14,15,13)(16,17), (10,16,13,11)(12,17,14,15), (10,17,13,11)(12,16,14,15), (1,5,9,4)(2,6,7,3), (1,4,3,6)(2,9,8,5)(10,12)(11,15)(13,14)(16,17), (1,3)(2,8)(4,6)(5,9)(10,14,12,13)(11,17,15,16), (1,6)(2,3)(4,8)(7,9)(10,17,14,11)(12,16,13,15), (2,4)(3,7)(5,6)(8,9)(10,17,15,14)(11,13,12,16), (1,9)(2,7)(3,6)(4,5)(10,13,12,14)(16,17), (1,7,8,5)(2,4,6,3)(10,17)(11,13)(12,16)(14,15), (1,5,7,2)(4,6,9,8)(10,12)(16,17), (2,6,4,5)(3,9,7,8)(10,11)(12,15)(13,16)(14,17), (3,7)(5,8)(6,9)(10,16,12,17)(11,13,15,14), (2,7,4,3)(5,8,6,9)(10,11,12,15)(13,16,14,17), (1,8,2,5)(3,6,9,7)(13,16)(14,17), (1,6,9,3)(2,4,7,5)(10,17)(11,15)(12,16)(13,14), (1,4)(3,8)(5,7)(10,13,17,11)(12,14,16,15), (1,8)(2,5)(6,7)(10,15,13,17)(11,14,16,12), (1,2)(5,7)(6,8)(10,12)(11,14,15,13), (1,4,8,3)(2,5,6,7)(10,17,12,16)(11,15), (1,9,2,3)(5,7,8,6)(10,15,17,13)(11,16,14,12), (1,6,7,8)(2,9,5,4)(10,17,14,15)(11,12,16,13), (1,4,2)(3,8,6)(5,9,7)(10,12)(11,15)(13,14)(16,17), (3,8,6)(5,7,9)(10,12)(11,15)(13,14)(16,17), (10,11,13,12,15,14)(16,17), (1,4,2)(3,8,6)(5,9,7)(11,15)(13,14), (1,4,2)(3,8,6)(5,9,7)(10,13)(11,16)(12,14)(15,17), (1,4,2)(3,8,6)(5,9,7)(10,13)(11,17)(12,14)(15,16), (1,6,3)(2,9,4)(5,8,7)(10,12)(11,15)(13,14)(16,17), (2,3,8,4,7,9)(5,6), (2,3,8,4,7,9)(5,6)(10,12)(11,15)(13,14)(16,17), (1,2,3,6,7,9)(4,5,8), (1,2,3,6,7,9)(4,5,8)(10,12)(11,15)(13,14)(16,17), (1,2,4)(3,6,8)(5,7,9)(13,16)(14,17), (1,2,4)(3,6,8)(5,7,9)(10,11)(12,15)(13,14)(16,17), (1,8,9)(2,5,3)(10,12)(16,17), (1,8,9)(4,7,6)(10,14)(11,16)(12,13)(15,17), (1,8,9)(4,7,6)(10,14)(11,17)(12,13)(15,16), (1,2,4)(3,6,8)(5,7,9)(10,11,13,12,15,14)(16,17), (3,6,8)(5,9,7)(13,16)(14,17), (3,6,8)(5,9,7)(10,11)(12,15)(13,14)(16,17), (2,4)(3,7)(5,6)(8,9)(10,11,13,12,15,14)(16,17), (1,5,7)(2,4,8)(3,6,9)(11,15)(13,14), (1,2)(3,9)(5,8)(6,7)(10,14,17)(12,13,16), (1,4,5)(2,8,6)(3,9,7)(10,13)(11,16)(12,14)(15,17), (1,3,9)(2,6,5)(4,8,7)(10,17)(11,13)(12,16)(14,15), (1,7,3)(2,5,6,4,9,8)(11,15)(16,17), (1,9)(2,4,3,7,5,6)(10,17)(11,14)(12,16)(13,15), (1,2,3,9,7,6)(4,5)(13,14)(16,17), (1,4,9,6,8,7)(2,3)(10,13)(11,17)(12,14)(15,16), (1,3,7)(2,8,9,4,6,5)(10,17)(11,14)(12,16)(13,15), (1,4,5,9,6,3)(2,8,7)(10,17)(11,13)(12,16)(14,15), (1,2,7)(3,4,8)(5,6,9)(10,13)(12,14), (1,9,5)(2,4,3)(6,8,7)(10,17)(11,15)(12,16)(13,14), (2,5,3)(4,6,7)(10,12)(11,17,13,15,16,14), (1,3,7)(2,8,9,4,6,5)(10,17)(11,15)(12,16)(13,14), (1,5,4,9,2,7)(3,6,8)(10,15)(11,12), (2,8,6,4,9,5)(3,7)(10,12)(11,13)(14,15)(16,17), (1,7)(2,4,6,5,9,8)(13,17)(14,16), (1,4)(3,8)(5,7)(10,11,14)(12,15,13), (1,2)(3,6)(7,9)(10,15,13,12,11,14)(16,17), (1,2,7)(3,4,8)(5,6,9)(10,15,13,12,11,14)(16,17), (2,7,5,4,3,6)(8,9)(10,16,13,12,17,14)(11,15), (1,5,7,8,3,4)(2,6,9)(10,13,11,12,14,15)(16,17), (1,3,6,9,5,4)(2,7,8)(10,15,16)(11,17,12), (1,3,5,9,6,4)(2,7)(10,17,13)(12,16,14), (1,6,7,5,4,9,8,3), (1,3,8,9,4,5,7,6), (2,3,6,9,4,7,5,8)(10,12)(11,15)(13,14)(16,17), (2,8,5,7,4,9,6,3)(10,12)(11,15)(13,14)(16,17), (1,2,5,6,9,7,4,3)(10,17)(11,13)(12,16)(14,15), (1,3,4,7,9,6,5,2)(10,17)(11,13)(12,16)(14,15), (1,7,4,3,6,9,8,2)(10,12)(11,15), (1,2,8,9,6,3,4,7)(10,12)(11,15), (1,8,4,2,7,6,9,5)(10,13)(11,16)(12,14)(15,17), (1,5,9,6,7,2,4,8)(10,13)(11,16)(12,14)(15,17), (1,5,4,2,3,9,6,8)(10,15,12,11)(13,16,14,17), (1,8,6,9,3,2,4,5)(10,11,12,15)(13,17,14,16), (1,2,6,4,9,7,3,5)(10,17)(11,15)(12,16)(13,14), (1,5,3,7,9,4,6,2)(10,17)(11,15)(12,16)(13,14), (1,3,8,7,6,2,4,9)(11,16)(15,17), (1,9,4,2,6,7,8,3)(11,16)(15,17), (1,6,7,3,8,2,5,4)(10,13,17,11)(12,14,16,15), (1,4,5,2,8,3,7,6)(10,11,17,13)(12,15,16,14), (1,9,5,8,7,4,2,6)(10,16,12,17)(13,14), (1,6,2,4,7,8,5,9)(10,17,12,16)(13,14), (2,3,6,9,4,7,5,8)(10,14,11,17)(12,13,15,16), (2,8,5,7,4,9,6,3)(10,17,11,14)(12,16,15,13), (1,2,4)(3,6,8)(5,7,9)(10,11,12,15)(13,16,14,17), (1,2,4)(3,6,8)(5,7,9)(11,13,15,14)(16,17), (1,2,4)(3,6,8)(5,7,9)(10,11,13,16)(12,15,14,17), (1,2,4)(3,6,8)(5,7,9)(10,11,13,17)(12,15,14,16), (3,6,8)(5,9,7)(10,11,12,15)(13,16,14,17), (1,3,6)(2,4,9)(5,7,8)(10,17,12,16)(11,14,15,13), (1,9,8)(2,3,5)(10,17,12,16)(13,14), (1,9,8)(4,6,7)(10,15,14,17)(11,13,16,12), (3,8,6)(5,7,9)(10,16,14,15)(11,12,17,13), (1,8,4,3,2,6)(5,9)(10,13,12,14)(11,16,15,17), (1,4,2)(3,5,6,7,8,9)(10,17,12,16)(11,14,15,13), (1,7,5)(2,8,4)(3,9,6)(11,14,15,13)(16,17), (1,5,4)(2,6,8)(3,7,9)(10,17,13,15)(11,12,16,14), (1,9,3)(2,5,6)(4,7,8)(10,11,17,13)(12,15,16,14), (1,5,3,4,7,8)(2,9,6)(10,11,17,13)(12,15,16,14), (1,7,8,6,9,4)(2,3)(10,11,14,17)(12,15,13,16), (2,6,3,4,5,7)(8,9)(10,14,15,17)(11,16,12,13), (1,6,2,7)(3,5,9,8)(10,16,14,12,17,13)(11,15), (1,8,4,7)(3,9,5,6)(11,16,14)(13,15,17), (1,3,5,9,6,4)(2,7)(10,14,12,13)(16,17), (1,7,5,8,6,2)(3,9,4)(10,17,13,15)(11,12,16,14), (1,8,5,2,6,7)(3,9,4)(10,12)(11,13,15,14), (1,5,8,6,4,3,7,9)(11,14,16)(13,17,15), (1,9,7,3,4,6,8,5)(11,16,14)(13,15,17), (2,9,5,3,4,8,6,7)(10,16,13,12,17,14)(11,15), (2,7,6,8,4,3,5,9)(10,14,17,12,13,16)(11,15)];
chartbl_82944_gr.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143];
chartbl_82944_gr.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 22, 23, 24, 25, 26, 27, 28, 2, 3, 4, 5, 6, 6, 2, 4, 5, 3, 6, 6, 6, 2, 7, 6, 6, 5, 4, 3, 13, 12, 14, 22, 23, 24, 22, 22, 22, 25, 23, 23, 22, 22, 22, 22, 23, 23, 23, 26, 23, 23, 24, 25, 24, 25, 25, 22, 23, 23, 23, 22, 22, 25, 25, 27, 22, 22, 23, 23, 24, 24, 28, 27, 26, 26, 27, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 33, 33, 33, 33, 39, 39, 40, 40, 41, 41, 52, 55, 56, 57, 53, 58, 65, 66, 67, 53, 52, 72, 74, 75, 57, 67, 66, 73, 73, 65, 56, 55, 136, 136, 136, 136], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1, 1, 1, 1, 1, 1, 1, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 2, 2, 2, 3, 4, 5, 2, 6, 7, 10, 11, 8, 9, 3, 5, 4, 2, 8, 9, 7, 3, 6, 4, 5, 17, 12, 13, 14, 18, 19, 8, 9, 2, 20, 21, 15, 16, 10, 11, 2, 7, 11, 10, 6, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 29, 30, 31, 32, 29, 29, 30, 32, 31, 35, 42, 30, 31, 32, 46, 36, 37, 34, 33, 38, 47, 48, 96, 97, 98, 99]];
chartbl_82944_gr.SizesCentralizers:= [82944, 82944, 13824, 13824, 13824, 9216, 9216, 6912, 6912, 2304, 2304, 1536, 1536, 1536, 768, 768, 384, 384, 384, 192, 192, 10368, 3456, 2592, 1728, 324, 108, 54, 6912, 3456, 3456, 3456, 1536, 1536, 768, 384, 384, 384, 256, 256, 256, 192, 128, 128, 128, 96, 96, 96, 64, 64, 64, 10368, 3456, 2592, 1728, 1728, 1728, 1728, 1152, 1152, 1152, 1152, 864, 864, 576, 576, 576, 324, 288, 288, 288, 288, 288, 288, 288, 192, 192, 192, 192, 192, 192, 144, 144, 108, 96, 96, 96, 96, 72, 72, 54, 36, 36, 36, 36, 1536, 1536, 1536, 1536, 256, 256, 256, 256, 256, 256, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 864, 432, 432, 432, 288, 144, 144, 144, 144, 96, 96, 72, 72, 72, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48];
chartbl_82944_gr.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "4U", "4V", "4W", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "6AN", "6AO", "6AP", "6AQ", "6AR", "8A1", "8A-1", "8B1", "8B-1", "8C1", "8C-1", "8D1", "8D-1", "8E1", "8E-1", "8F1", "8F-1", "8G1", "8G-1", "8H1", "8H-1", "8I1", "8I-1", "8J1", "8J-1", "8K1", "8K-1", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H", "12I", "12J", "12K", "12L", "12M", "12N", "12O", "12P", "12Q", "12R", "12S", "12T", "12U", "12V", "24A1", "24A-1", "24B1", "24B-1"];
chartbl_82944_gr.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24];
chartbl_82944_gr.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1], [1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 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ConvertToLibraryCharacterTableNC(chartbl_82944_gr);